More math help questions--test tomorrow. :) ?

Question

Thank you to those who helped me last time, it was very helpful. :) But now I'm trying to do my other math problems, and am yet again stuck.

1. A total of $900,000 is to be divided up among Paige, David and Dan. Paige is to receive 3/4 of what David gets, while Dan gets 1/2 of what David gets. How much does each receive?

I've tried this one so many times, but nothing adds up to 900,000.

2. A 20 pound bag of cement has 25% cement and 75% sand. How much cement must be added to produce a cement mix with 40% cement?

Now, the answer is 5 pounds, but I keep coming up with really weird answers.

I set it up like this: .25(20)/(20-x)

But that doesn't get me five. Once I tried it and ended up with a quadratic, which got me a negative number...so...if anyone knows how to properly set that up...

3. One pump can empty a tank in 4 hours. Another can do it in 9. If the first pump is started at 9 AM, when should the other be started so the tank can be emptied by noon?

For this one, I did the basic combined work equation, but obviously that doesn't quite work...so I tried doing 1/4 + 1/9 = 13/36...but that isn't working one bit. I end up with some really huge fraction...and the answer, I checked, is a simple number. So I don't know what I've done wrong there.

4. One pipe takes 6 hours to fill a tank, and another empties it in 8. If both are open, how long will it take to fill the tank?

Yes, again with this one...I tried the combined work one again.

5. The length of a rectangle is 2 ft more than its width. If the width were increased by 4 ft and the length diminished by 3, the area would increase by 49 ft. What are the new dimensions?

I set this one up about twelve different ways, but I keep getting zero. I know it can't be zero. :(

Okay, five questions...sorry if it's long. =/

Anyway, again, not looking for answers, but I do need to know where I've gone wrong in setting these up.

Thank you to anyone who can understand this!

Answer 1

P = Paige

D = David

N = Dan

P =(3/4)D

N = (1/2)D

P + D + N = 900,000

Three equations, three unknowns. Pretty simple. Use substitution to solve the system of equations:

D = 900,000 - P - N

D = 900,000 - (3/4)D - (1/2)D

D + (3/4)D + (1/2)D = 900,000

(4/4)D + (3/4)D + (2/4)D = 900,000

(9/4)D = 900,000

D = (4/9)(900,000)

D = 4(100,000)

D = $400,000

Then, simply substitute D = 400,000 to solve the other two values:

P = (3/4)D

P = (3/4) (400,000)

P = 3(100,000)

P = $300,000

N = (1/2)D

N = (1/2)(400,000)

N = $200,000

Therefore,

D = $400,000

P = $300,000

N = $200,000

Answer 2

1.

Let's say David gets "x".

Paige gets 3/4 x

Dan gets 1/2 x

And we know that David + Paige + Dan = 900,000

So, x + .5 x + .75 x = 900,000

I'm sure you can take it from there.

2.

So initially, it has 5 pounds of cement and 15 pounds of sand, right?  And if at the end, it's 40 percent cement, then it will be 60 percent sand.  So it's asking: 15 pounds = 60 percent of x...what's x?

3.

Ok, so on its own, the first pump could get the tank 3/4 of the way empty by noon, right?  So it's asking "pump 2 can empty the tank 1/9 of the way per hour.  How many hours would it need in order to take care of the 1/4 of the tank that pump 1 can't handle?"  Or, "1/9 times what = 1/4?"

4.

So for each hour, pipe A fills the tank 1/6 of the way, and pipe B empties out 1/8 of however much the tank can hold.

1/6 = 8/48

1/8 = 6/48

So each hour, the net effect is that the tank is filling by 2/48 (which is 1/24).

5.

L = W + 2

(W + 4) x (L - 3) = 49 + (L x W)

If you write out the 2nd equation but replace every "L" with "(W+2)" (since the first equation tells us they're the same, and note that I said "(W+2)", not "W+2" - it will help you to not make mistakes), it should be easy enough to solve for W.